The Abbott government should slash the ABC, lower taxes, forget the medical research fund and stop paying millions to search for Malaysian flight MH370, says Liberal Senator Cory Bernardi.

On the same day shadow treasurer Chris Bowen gave his budget reply speech, Senator Bernardi has delivered the bluntest assessment of the Abbott government's first budget yet seen by a Coalition MP.

"There are plenty of regular people who are disappointed with aspects of the budget and their concerns are entirely legitimate," Senator Bernardi writes in a letter to his supporters.

Why, Senator Bernardi asks, was not more funding cut from the ABC? "If it was up to me I'd limit the ABC's public funding to current radio stations and two television channels," he writes.

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"Other than that they should have to compete on commercial terms. This could save the taxpayer hundreds of millions of dollars per year." The Abbott government's budget cuts to the ABC and SBS – combined savings of $43.5 million over four years – were much gentler than the expected $250 million in cuts that would have resulted from an efficiency dividend. More cuts are expected, however, when Communications Minister Malcolm Turnbull releases the findings of an "efficiency study" into the ABC and SBS.

Senator Bernardi says he has "no idea" why the Abbott government is contributing as much as $90 million towards the search for missing Malaysia Airlines Flight MH370. And he remains unhappy about the debt tax, saying he would prefer a reduction in taxes and in the size of government.

"But for better or worse, this is what the government decided," he writes.

Dismissing the budget reaction of "socialist university students" and "Labor activists", Senator Bernardi has defended the Abbott government's tightening of unemployment benefits and $8 billion in cuts to foreign aid. He supports lifting the retirement age to 70, adding that "if we do not make these changes Australia will be setting itself up to have an unsustainable welfare system."

But Senator Bernardi questions why Treasurer Joe Hockey is putting money saved from the $7 GP fee into a medical research fund rather than reducing Labor's debt.

"Personally, I would prefer to see the co-payment directed to debt reduction but the government decided otherwise," he writes.

He said it was "good news" that the budget had abolished the Australian Renewable Energy Agency and that the government was "still committed to abolishing the Climate Change Authority and the Clean Energy Finance Corporation".

"There is probably scope and justification to abolish more of these bodies established through … alarmism but this is a good start." Other Coalition backbenchers, including western Sydney MP Craig Laundy, say they will be conveying concerns about the budget from their constituents when they return to Canberra next week. But none have delivered a message as critical or comprehensive as Senator Bernardi's.

With the Abbott government facing opposition from Labor, the Greens and the Palmer United Party to many of their policies, Senator Bernardi concedes that "the government will have to make some concessions as the Senate is unlikely to pass all the budget measures." Independent Senator Nick Xenophon has warned Prime Minister Tony Abbott that his "dumb" budget is toxic with many Coalition voters.

"This has been called the toughest budget in decades, but it also seems to be one of the dumbest," the South Australian independent wrote in a budget appraisal.

"The 'Howard Battlers' that re-elected John Howard on four occasions won't cop these changes." Senator Xenophon is one of eight crossbenchers who will hold the balance of power in the Senate from July 1.